Spiking neural P (SNP) systems are a class of neural-like computing models, abstracted by the mechanism of spiking neurons. This article proposes a new variant of SNP systems, called gated spiking neural P (GSNP) systems, which are composed of gated neurons. Two gated mechanisms are introduced in the nonlinear spiking mechanism of GSNP systems, consisting of a reset gate and a consumption gate. The two gates are used to control the updating of states in neurons. Based on gated neurons, a prediction model for time series is developed, known as the GSNP model. Several benchmark univariate and multivariate time series are used to evaluate the proposed GSNP model and to compare several state-of-the-art prediction models. The comparison results demonstrate the availability and effectiveness of GSNP for time series forecasting.

Membrane computing is an unconventional computing paradigm that has gained much attention in recent decades because of its massively parallel character and its usefulness to build models of complex systems. However, until now, there was no generic hardware implementation of P systems. Computational frameworks to execute P systems up to this day rely on the simulation of the parallel working mechanisms of P systems by inherently sequential algorithms. Such algorithms can then be implemented as is or can be parallelized, up to a certain point, to run on parallel computers. However, this is not as efficient as a dedicated parallel hardware implementation. There have been ad hoc implementations of particular P systems for parallel hardware, but they lack to be problem-generic or they are not scalable enough to implement large P systems. In this paper, a first intrinsically parallel hardware architecture to implement generic P system models is introduced. It is designed to be straightforwardly implemented in programmable logic circuits like FPGAs. The feasibility and correct execution of our architecture has been verified by means of a simulator, and several simulation results for different P system examples have been analysed to foresee the pros and cons of this design.

Membrane computing is a massively parallel and non-deterministic bioinspired computing paradigm whose models are called P systems. Validating and testing such models is a challenge which is being overcome by developing simulators. Regardless of their heterogeneity, such simulators require to read and interpret the models to be simulated. To this end, P-Lingua is a high-level P system definition language which has been widely used in the last decade. The P-Lingua ecosystem includes not only the language, but also libraries and software tools for parsing and simulating membrane computing models. Each version of P-Lingua supported new types or variants of P systems. This leads to a shortcoming: Only a predefined list of variants can be used, thus making it difficult for researchers to study custom ones. Moreover, derivation modes cannot be user-defined, i.e, the way in which P system computations should be generated is determined by the simulation algorithm in the source code. The main contribution of this paper is a completely new design of the P-Lingua language, called P-Lingua 5, in which the user can define custom variants and derivation modes, among other improvements such as including procedural programming and simulation directives. It is worth mentioning that it has backward-compatibility with previous versions of the language. A completely new set of command-line tools is provided for parsing and simulating P-Lingua 5 files. Finally, several examples are included in this paper covering the most common P system types.

Coupled neural P (CNP) systems are a recently developed Turing-universal, distributed and parallel computing model, combining the spiking and coupled mechanisms of neurons. This paper focuses on how to apply CNP systems to handle the fusion of multi-modality medical images and proposes a novel image fusion method. Based on two CNP systems with local topology, an image fusion framework in nonsubsampled shearlet transform (NSST) domain is designed, where the two CNP systems are used to control the fusion of low-frequency NSST coefficients. The proposed fusion method is evaluated on 20 pairs of multi-modality medical images and compared with seven previous fusion methods and two deep-learning-based fusion methods. Quantitative and qualitative experimental results demonstrate the advantage of the proposed fusion method in terms of visual quality and fusion performance.

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP-ECR systems). SNP-ECR systems are a class of distributed parallel computing models. In SNP-ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP-ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP-ECR systems. It is proven that SNP-ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP-ECR system as function computing devices.

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered.

Biological membranes play an active role in the evolution of cells over time. In the framework of Membrane Computing, P systems with active membranes capture this idea, and the possibility to increase the number of membranes during a computation. Classically, it has been considered, by using divisi on rules, inspired in the mitosis process. Initially, the membranes in these models are supposed to have an electrical polarization (positive, negative or neutral) and the semantics is minimalist, in the sense that rules are applied in parallel, but in one transition step, each membrane can be the subject of at most one rule of types communication, dissolution or division. This paper focuses on polarizationless P systems with active membranes in which membrane creation rules are considered instead of membrane division rules as a mechanism to construct an exponential workspace, expressed both in terms of number of objects and membranes, in linear time. Moreover, the minimalist semantics is considered and some complexity results are provided in this framework, allowing to tackle the P versus NP problem from a new perspective. An original frontier of the efficiency in this context is unveiled in this paper: allowing membrane creation rules to be applicable in any membrane of the system, instead of restricting them to only elementary membranes, yields a significant boost on the computational power. More precisely, only problems in P can be efficiently solved in the restricted case, while in the non-restricted case an efficient and uniform solution to a PSPACE-complete problem is provided.

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron's firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively.

Polarizationless P systems with active membranes are non-cooperative systems, that is, the left-hand side of their rules have a single object. Usually, these systems make use of division rules as a mechanism to produce an exponential workspace in linear time. Division rules are inspired by cell div ision, a process of nuclear division that occurs when a parent cell divides to produce two identical daughter cells. On the other hand, separation rules are inspired by the membrane fission process, a mechanism by which a biological membrane is split into two new ones in such a manner that the contents of the initial membrane is distributed between the new membranes. In this paper, separation rules are used instead of division rules. The computational efficiency of these models is studied and the role of the (minimal) cooperation in object evolution rules is explored from a computational complexity point of view.

Membrane computing is a computing paradigm providing a class of distributed parallel computing devices of a biochemical type whose process units represent biological membranes. In the cell-like basic model, a hierarchical membrane structure formally described by a rooted tree is considered. It is w ell known that families of such systems where the number of membranes can only decrease during a computation (for instance by dissolving membranes), can only solve in polynomial time problems in class P. P systems with active membranes is a variant where membranes play a central role in their dynamics. In the seminal version, membranes have an electrical polarization (positive, negative, or neutral) associated in any instant, and besides being dissolved, they can also replicate by using division rules. These systems are computationally universal, that is, equivalent in power to deterministic Turing machines, and computationally efficient, that is, able to solve computationally hard problems in polynomial time. If polarizations in membranes are removed and dissolution rules are forbidden, then only problems in class P can be solved in polynomial time by these systems (even in the case when division rules for non-elementary membranes are permitted). In that framework it has been shown that by considering minimal cooperation (left-hand side of such rules consists of at most two symbols) and minimal production (only one object is produced by the application of such rules) in object evolution rules, such systems provide efficient solutions to NP-complete problems. In this paper, minimal cooperation and minimal production in communication rules instead of object evolution rules is studied, and the computational efficiency of these systems is obtained in the case where division rules for non-elementary membranes are permitted.

This paper focuses on automatic fuzzy clustering problem and proposes a novel automatic fuzzy clustering method that employs an extended membrane system with active membranes that has been designed as its computing framework. The extended membrane system has a dynamic membrane structure; since membranes can evolve, it is particularly suitable for processing the automatic fuzzy clustering problem. A modification of a differential evolution (DE) mechanism was developed as evolution rules for objects according to membrane structure and object communication mechanisms. Under the control of both the object's evolution-communication mechanism and the membrane evolution mechanism, the extended membrane system can effectively determine the most appropriate number of clusters as well as the corresponding optimal cluster centers. The proposed method was evaluated over 13 benchmark problems and was compared with four state-of-the-art automatic clustering methods, two recently developed clustering methods and six classification techniques. The comparison results demonstrate the superiority of the proposed method in terms of effectiveness and robustness.

P systems have been proven to be useful as modeling tools in many fields, such as Systems Biology and Ecological Modeling. For such applications, the acceleration of P system simulation is often desired, given the computational needs derived from the

on the occasion of his 65th birthday.

Sevilla carpets have already been used to compare different solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets in this context, and a script that allows to generate them automatically from P-Lingua files.

In 1936 A. Turing showed the existence of a universal machine able to simulate any Turing machine given its description. In 1956, C. Shannon formulated for the first time the problem of finding the smallest possible universal Turing machine according to some critera to measure its size such as the number of states and symbols. Within the framework of Membrane Computing different studies have addressed this problem: small universal symport/antiport P systems (by considering the number of membranes, the weight of the rules and the number of objects as a measure of the size of the system), small universal splicing P systems (by considering the number of rules as a measure of the size of the system), and small universal spiking neural P systems (by considering the number of neurons as a measure of the size of the system). In this paper the problem of determining the smallest possible efficient P system is explicitly formulated. Efficiency within the framework of Membrane Computing refers to the capability of solving computationally hard problems (i.e. problems such that classical electronic computer cannot solve instances of medium/large size in any reasonable amount of time) in polynomial time. A descriptive measure to define precisely the notion of small P system is presented in this paper.

Cell-like recognizing membrane systems are computational devices in the framework of membrane computing inspired from the structure of living cells, where biological membranes are arranged hierarchically. In this paper tissue-like recognizing membrane systems are presented. The idea is to consider that membranes are placed in the nodes of a graph, mimicking the cell intercommunication in tissues. In this context, polynomial complexity classes associated with recognizing membrane systems can be defined. We recall the definition for cell-like systems, and we introduce the corresponding complexity classes for the tissue-like case. Moreover, in this paper two efficient solutions to the satisfiability problem are analyzed and compared from a complexity point of view. © 2009 Wiley Periodicals, Inc.